条（环）状干摩擦阻尼器的微滑移数值模型

摘要

提出一种求解弹性条（环）状阻尼器微滑移接触运动的数值方法。将阻尼器和外部激励历程在空间和时间上离散，将相同数量的干摩擦触点布置于离散阻尼器上；把接触运动判据应用到各离散接触点，确定其运动状态并修正刚度矩阵，求解整个阻尼器的平衡方程。该方法避免了有限元软件求解含摩擦接触问题的迭代过程，从而保证了求解的可执行性。同时，克服了微滑移模型理论解法对法向载荷分布规律及载荷时变性的限制，为求解具有局部性以及时变性的法向载荷的结构动态响应提供了更为精确的边界条件，从而可提高结构频响分析的准确性。应用多谐波平衡法分别计算宏滑移和微滑移阻尼器约束下的结构动态响应，发现在结构减振中，微滑移模型能够适应更宽范围的法向力。%A numerical method to solve the contact kinematic problems of elastic bar or circular micro-slip dry friction damper was proposed. Firstly,the damper and the time course of external excitation were discretized in the space and time domain respectively,and the same number of contact points was attached to the discrete damper.Secondly,the determination criterion of the contact kinematic state of the contact point pairs was used to each contact pair,and the stiffness matrix of the damper was modified.Thirdly,the whole balance equation with the new stiffness matrix was solved in each time step.Differing from the way the finite element software dealing with the contact problem with friction,the iteration was avoided,thus the feasibility of the solution was guaranteed.Meanwhile,the restriction of the distribution and the time variability of the normal load was overcome,and therefore it provided a more accurate boundary condition for solving dynamic response of structure.Lastly,the response of structures constrained by the macro-slip and micro-slip damper were computed by the MHBM(Multi Harmonic Balance Method)respectively and the distinctness of the solution was analyzed.Results show that the micro-slip model damper can have a broader normal force range for vibration reduction.